Mathematics – Probability
Scientific paper
2009-09-09
Mathematics
Probability
This is a corrected version. An error in Proposition 3.2 is corrected and hence technical assumptions in Theorem 1.1 and Corol
Scientific paper
In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions and smooth explicit approximations for a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The discretization is given in terms of discrete-jumping filtrations which allow us to approximate non-smooth processes by means of a stochastic derivative operator on Wiener space. As a by-product, we provide a robust semimartingale approximation for weak Dirichlet-type processes. The underlying semimartingale skeleton is intrinsically constructed in such way that all the relevant structure is amenable to a robust numerical scheme. In order to illustrate the results, we provide an easily implementable approximation scheme for the classical Clark-Ocone formula in full generality. Unlike in previous works our methodology does not assume an underlying Markovian structure and requires no use of Malliavin weights. We conclude by proposing a method which enables to compute optimal stopping times in a non-Markovian setup arising e.g. from the fractional Brownian motion.
Leao Dorival
Ohashi Alberto
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